By this time the student should have found himself sufficiently prepared to take up problems of rotational motion. The application of Newton's Laws to pure rotations and combinations of rotation and translation, such as rolling motions, are very many. We would emphasize here the dynamic definition of moment of inertia, I = Fh/_a_ rather than the one so frequently given importance for computational purposes, S_mr_^{ 2}. Quantitative experiments are furnished by the rotational counterpart of the Atwood machine. Lecture demonstrations for several talks abound: stability of spin about the axis of greatest inertia, Kelvin's famous experiments with eggs and tops containing liquids, which suggest the gyroscopic ideas, and finally a discussion of gyroscopes and their multitudinous applications. The book of Crabtree, _Spinning Tops and the Gyroscope_, and the several papers by Gray in the _Proceedings of the Physical Society of London_, summarize a wealth of material. If one wishes to interject a parenthetical discussion of the Bernouilli principle, and the simplest laws of pressure distributions on plane surfaces moving through a resisting medium, a group of striking demonstrations is possible involving this notion, and by simple combination of it with the precession of a rotating body the boomerang may be brought in and its action for the major part given explanation.
Rotational motion leads naturally to a discussion of centripetal force, and this in turn is simple harmonic motion. This latter finds most important applications in the pendulum experiments, and no end of material is here to be found in any of the textbooks. The greatest refinement of experimentation for elementary purposes will be the determination of "g" by the method of coincidences between a simple pendulum and the standard clock. Elementary analysis without use of calculus reaches its culmination in a discussion of forced vibrations similar to that used by Magie in his general text. Many will not care to go as far as this. Others will go farther and discuss Kater's pendulum and the small corrections needed for precision, for here does precision find bold expression.
It is not our purpose to give a synopsis of the entire general physics course. We have made an especially detailed study of mechanics, because this topic is the one of greatest difficulty by far in the pedagogy. It is too formally given in the average text, and seems to have suffered most of all from lack of imagination on the part of instructors.
